PO005 EVALUATION OF SHIFT FORMULAE IN CIELAB AND CAM02

Dorukalp Durmus et al.

DOI 10.25039/x46.2019.PO005

from

CIE x046:2019 Proceedings of the 29th CIE SESSION Washington D.C., USA, June 14 – 22, 2019 (DOI 10.25039/x46.2019)

The paper has been presented at the 29th CIE Session, Washington D.C., USA, June 14-22, 2019. It has not been peer-reviewed by CIE.  CIE 2019 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from CIE Central Bureau at the address below. Any mention of organizations or products does not imply endorsement by the CIE. This paper is made available open access for individual use. However, in all other cases all rights are reserved unless explicit permission is sought from and given by the CIE. CIE Central Bureau Babenbergerstrasse 9 A-1010 Vienna Austria Tel.: +43 1 714 3187 e-mail: [email protected] www.cie.co.at Durmus, D., Davis, W. EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02

EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02

Dorukalp Durmus1,2, Wendy Davis1 1Sydney School of Architecture, Design and Planning, the University of Sydney, AUSTRALIA 2Pacific Northwest National Laboratory, Portland, USA [email protected]

DOI 10.25039/x46.2019.PO005

Abstract

Calculated hue shifts could vary widely for spectrally similar light sources, which suggests a limitation of the current hue shift formulae for non- light sources. Calculated differences in the hue appearance of 24 colour samples under 279,936 iteratively-generated test SPDs versus two reference illuminants were compared using four hue shift formulae that are based on two widely used colour spaces, CIE 1976 L* a* b* (CIELAB) and colour appearance model 2002 (CAM02). Hue shift equations did not correlate well, even when only nominally “white” light sources were considered. Results suggest that the underlying difference between the hue shift formulae might be the non-uniform scaling of redness-greenness (a) and yellowness-blueness (b) coordinates in CIELAB and CAM02-UCS. A chromatic adaptation transform correction improved the correlation between lightness in CIELAB and CAM02-UCS when the test light sources were nominally “white,” but caused irregularities for non-white light sources. Further research is needed for visual assessment of the hue shifts and to evaluate the hue shift formulae.

Keywords: , Colour, Hue, Colour Appearance Model, Chromatic Adaptation

1 Introduction

The colour appearance of objects can be quantified using three-dimensional colour spaces. The three dimensions of a colour space are typically lightness, colourfulness, and hue. Lightness can be described as the brightness of a surface, and colourfulness indicates the strength of the chromatic content (e.g. redness of a object). The International Commission on Illumination (CIE) describes hue as the “attribute of a visual perception according to which an area appears to be similar to one of the colours: red, , green, and ” (CIE, 2011), which is categorically different from lightness and colourfulness for inexperienced observers. Humans are typically more sensitive to hue shifts than changes in saturation and lightness (Danilova and Mollon, 2016). Although hue can be calculated using colour appearance models (CAMs)— mathematical models quantifying the perceptual attributes of coloured stimuli— hue is not widely used to quantify object colours in architectural lighting practice and research.

Hue angle (h) and hue (H) differences can be calculated in two of most widely used colour spaces: CIE 1976 L*a*b* (CIELAB) and CAM02 (CIE, 2018). In both colour spaces, hue angle is calculated h = arctan (b/a), which is between 0 and 360 degrees and corresponds to the hue circle. Since a is the redness-greenness and b is the yellowness-blueness component, h = 0 approximates the appearance of red, h = 90 yellow, h = 180 green, and h = 270 blue object surfaces. The hue difference (H) in CIELAB and CAM02-UCS is calculated using hue angle (h) and chroma values (CIE, 2018).

A recent study showed that the calculated hue differences (H) can vary greatly even when the total calculated colour difference is small (Durmus and Davis, 2018). Although in this study large calculated hue shifts in CAM02 uniform colour space (CAM02-UCS) under a reference white illuminant and optimised non-white light source were found (Durmus and Davis, 2018), other studies did not find similar large hue shifts in CIELAB under a reference white illuminant and optimised non-white light sources (Durmus et al., 2018; Abdalla et al., 2016). It is possible that the reference illuminant and the colour space differences cause abnormality in hue shift calculations for highly structured spectral power distributions (SPDs), especially when the light

888 Proceedings of 29th CIE Session 2019 Durmus, D., Davis, W. EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02 source deviates from the Planckian locus. Here, hue shift calculations under a large combination of test SPDs are compared to investigate the underlying issue.

2 Methods

Differences in hue was calculated for 24 Macbeth ColorChecker samples under test and reference conditions using four formulae, two formulae in each colour space (CIELAB and CAM02). Two reference SPDs were considered: CIE D50 and a white phosphor-converted LED (pcLED). Test SPDs were created by iteratively mixing seven narrowband channels of the Source Four LED Profile x7 Colour System™ in six steps of DMX control signal (0%, 20%, 40%, 60%, 80%, and 100%) for each LED channel, a total of 279,936 combinations. For example, one test SPD consisted of 0% LED channel 1, 20% LED channel 2, 60% LED channel 3, 80% LED channel 4, 100% LED channel 5, 0% LED channel 6, and 40% LED channel 7. All test SPDs were compared to each reference SPD. The radiant power of the test SPDs were adjusted to equalise the luminance of the sample in the reference and test conditions, to prevent changes in hue and chroma caused by luminance differences (Hunt and Pointer, 2011).

Hue shifts were calculated using four formulae, all based on Séve’s hue shift calculations (1991). The first formula,

* **1/2 HChSeve  2(C12 ) sin( / 2) (1) where

C = (a*2+b*2)1/2 is the chroma; h is the hue angle; is recommended by the CIE to calculate hue shifts (CIE, 2018). The second formula was an alternative method offered by Stokes and Brill (1992),

***1/2** HsQaabbSB [2( 12 12] (2) where

* * *2 *2 *2 *2 1/2 Q = C1 C2 = [(a1 +b1 ) (a2 +b2 )] ab** ab ** s 1, if  12 21 otherwise s 1, to calculate hue shifts more efficiently (to reduce computation time) in CIELAB. The third and fourth methods were Séve’s hue shift formula applied to CAM02. The typical CAM02 parameter 2 settings (LA = 60 cd/m , SR = 1, surround = average) for the “surface colour evaluation in a light booth” (Luo and Li, 2013) were used to enable visual evaluations of the computational results in the future. Although a hue shift formula was not proposed in the original CAM02, hue shift formulae can be adapted to other colour spaces (Luo et al., 2006) and CAM02

* HCAM02,mod1  2sin(/2)CC12 h (3) and

*'' HCAM02,mod2  2sin(/2)MM12 h (4) where

C is the chroma; M' is the colourfulness.

* * H Seve and H CAM02,mod1 are based on chroma, C, and hue angle, h (calculated using a-b and * a'M -b'M coordinates, respectively). While chroma, and therefore H Seve, in CIELAB is solely dependent on a* and b* coordinates, CAM02 makes a distinction between colourfulness (M'),

Proceedings of 29th CIE Session 2019 889 Durmus, D., Davis, W. EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02 chroma (C), and saturation (s), and provides three outputs for this dimension that are not interchangeable (Luo and Li, 2013). The CIE defines chroma as “colourfulness of an area judged as a proportion of the brightness of a similarly illuminated area that appears white or highly transmitting” (2017). Since chroma is approximately constant across luminance changes, and colourfulness is an absolute perceptual quantity (i.e. changing with luminance) (Fairchild, 2013), it is possible that chroma (C*) in CIELAB corresponds to colourfulness instead of * * chroma. However, H CAM02,mod1 uses chroma instead of colourfulness. Unlike H Seve, in which chroma is not brightness dependent, in CAM02, the calculation of chroma includes lightness * and the achromatic response, as well as a' and b' coordinates. It is likely that H CAM02,mod1 is * affected by the chroma-colourfulness distinction in CAM02. To address this, H CAM02,mod1 was * modified by replacing chroma with colourfulness in CAM02 (H CAM02,mod2).

3 Results and discussion

Reference light source The minimum, maximum, average and standard deviation of the hue shifts for each colour sample were calculated. The minimum, maximum and average hue shifts for each sample were then averaged over all samples, as shown in Table 1. The average hue shift over all colour * * samples was H Seve,avg = -0.3 (H Seve,sd = 51.8) when the reference was D50 and was * * H Seve,avg = -0.1 (H Seve,sd = 51.4) when the reference was the pcLED. The average hue shift * * was H CAM02,mod1,avg = -2.0 (H CAM02,mod1,sd = 43.8) when the reference was D50 and was * * H CAM02,mod1,avg = -2.5 (H CAM02,mod1,sd = 43.0) when the reference was the pcLED.

Table 1 –The minimum (min.t) and maximum (max.t) hue shift over all colour samples of all SPDs, average (avg.avg), average of the minimum (avg.min), and average of the maximum (avg.max) hue shifts over all colour samples for the four hue shift formulae Reference D50 Reference pcLED

Min.t Max. t Avg. Avg. Avg. Min.t Max.t Avg.Avg. Avg. avg min max avg min max * H Seve -285 283 -0.3 -157 162 -372 332 0.1 -170 165 * H SB -280 257 -0.5 -123 111 -303 261 -1.6 -127 113 * H CAM02,mod1 -321 317 -2.0 -165 173 -351 414 -2.5 -170 161 * H CAM02,mod2 -116 114 -1.2 -71 72 -123 133 -1.5 -73 70 Calculated hue shifts varied slightly under two reference light sources. While the order of the * * range of hue shift difference was similar (i.e. H CAM02,mod1 range was the greatest, H CAM02,mod2 * range was the smallest), minimum hue shift was H Seve when the reference was pcLED. However, the difference in minimum, maximum, and average values were not as great as the difference between hue shift formulae.

When calculate hue shifts were investigated under reference D50 and pcLED, no correlation * was found between any of the hue shift equations for any sample. H CAM02,mod1 varied more (from -321 to 317 when the reference was D50, and from -351 to 414 when the reference was * pcLED) than H Seve (from -285 to 283 when the reference was D50, and from -372 to 332 when * the reference was pcLED). The hue shift formula H CAM02,mod2 showed the least variation (from -116 to 114 when the reference was D50, and from -123 to 133 when the reference was pcLED). Since highly chromatic lighting may cause large hue shift differences for low chroma surfaces (e.g. grey samples) (CIE, 2018), hue shifts for chromatic samples were compared to achromatic samples by grouping them according to their spectral reflectance shapes. A similar grouping was used in previous studies (Durmus and Davis, 2015a, 2015b, 2018), where peak were samples 3, 6, 11, 14, and 18, plateau were samples 1, 2, 7, 9, 12, 15, and 16, peak+incline were samples 4, 5, 8, 10, 13, 17, and plain were samples 19, 20, 21, 22, 23, and 24. Hue shifts for chromatic samples (peak, plateau, and peak+incline type reflectance) showed greater variation compared to achromatic samples (plain type reflectance), as shown in Table 2. These results are similar to previous findings (Durmus and Davis, 2018), which suggests that the hue shift anomalies are not due to axis-crossing (a-b axes) in low chroma object appearance.

890 Proceedings of 29th CIE Session 2019 Durmus, D., Davis, W. EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02

Table 2 –The average (avg.avg), average of the minimum (avg.min), and average of the maximum (avg.max) hue shifts for peak (samples 3, 6, 11, 14, and 18), plateau (samples 1, 2, 7, 9, 12, 15, and 16), peak+incline (samples 4, 5, 8, 10, 13, 17) and plain (samples 19, 20, 21, 22, 23, and 24) type reflectances for the four hue shift formulae Reference D50 Reference pcLED * * * * * * * * H Seve H SB H CAM H CAM H Seve H SB H CAM H CAM 02,mod1 02,mod2 02,mod1 02,mod2 Peak Avg 0 -13 1 0 0 -8 -2 -1 .avg Avg -209 -151 -246 -98 -216 -151 -239 -98 .min Avg 192 201 245 95 205 196 233 93 .max Plateau Avg -1 13 -4 -2 0 10 -10 -6 .avg Avg -197 -194 -208 -91 -203 -209 -218 -93 .min Avg 217 132 240 98 192 138 213 91 .max Peak + Avg 0 -5 -3 -2 0 -10 3 1 incline .avg Avg -205 -126 -203 -88 -244 -127 -215 -92 .min Avg 211 111 195 86 245 115 192 87 .max Plain Avg 0 -1 0 0 0 -2 0 0 .avg Avg -20 -16 -10 -8 -20 -13 -12 -8 .min Avg 22 14 11 8 19 12 11 8 .max

* The explanation for the wider range of values from H CAM02,mod1 could be the contribution of the lightness and achromatic response in the CAM02 hue calculations, since the reference and test a'M and b'M coordinates of CAM02-UCS varies less (-118 < a'M < 111, a'M,avg = 0.2, -39 < b'M < 50, b'M,avg = 0.6) compared to the a* and b* coordinates of CIELAB (-218 < a* < 532, a*avg = 13.3, -547 < b* < 164, b*avg = -15.6). On the other hand, the difference in these coordinates could also be attributed to the uniformity and scale differences between CIELAB and CAM02- UCS, especially in the positive a* and negative b* directions (Luo et al., 2006). For example, the CIELAB a*-b* coordinates (-50 < a* < 60, -50 < b* < 60) for the OSA data set (MacAdam, 1974) ranges slightly more compared to CAM02-UCS a'M-b'M (-30 < a'M < 40, -35 < b'M < 45) for the same data set (Luo et al.,2006). To test the impact of colour space uniformity and scale difference, calculated hue shifts for all SPDs were compared to those for only nominally “white” test light sources.

All test SPDs and nominally “white” test SPDs

When test SPDs were limited to nominally “white” light sources (close to the Planckian locus) according to ANSI specifications (ANSI, 2017), hue shifts calculated with CAM02-UCS were smaller than hue shifts calculated with CIELAB, as shown in Table 3. The range of lightness and a-b coordinates were similar under CIELAB and CAM02-UCS, as shown in Table 4. Calculated hue shifts for nominally “white” SPDs showed a smaller range compared to previous findings. However, when the test light sources were limited to be nominally “white,” the correlation between hue shift formulae did not improve.

Proceedings of 29th CIE Session 2019 891 Durmus, D., Davis, W. EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02

Table 3 –The minimum (min.t) and maximum (max.t) hue shift over all colour samples of nominally “white” light sources, average (avg.avg), average of the minimum (avg.min), and average of the maximum (avg.max) hue shifts over all colour samples for the four hue shift formulae Reference D50 Reference pcLED

Min.t Max. t Avg. Avg. Avg. Min.t Max.t Avg.Avg. Avg. avg min max avg min max * H Seve -204 194 -1.5 -92 92 -207 195 -1.4 -93 91 * H SB -66 72 -0.1 -29 29 -60 71 -1.4 -30 28 * H CAM02,mod1 -137 139 1.02 -74 75 -148 140 1.3 -75 74 * H CAM02,mod2 -77 78 6.2 -45 46 -78 78 0.8 -45 45

When hue shifts were calculated for all SPDs, average lightness values were similar (J'avg = 58, L*avg = 55). However, lightness in CAM02-UCS (J') ranged from 9 to 180, while lightness in CIELAB (L*), which is mathematically limited from 0 to 100, ranged from 21 to 96. When hue shifts were calculated only for nominally “white” test light sources, lightness range in CAM02- UCS (J'avg = 58, 24 < J' < 96) was similar to lightness range in CIELAB (L*avg = 55, 21 < L* < 95).

Table 4 –The average, minimum and maximum CIELAB and CAM02-UCS coordinates under all test SPDs and nominally “white” test light sources CIELAB CAM02-UCS

L* a* b* J' a'M b'M All test Avg. 55 -7 24 58 2 2 SPDs Max. 96 532 164 180 111 50 Min. 21 -218 -547 9 -118 -39 “White” Avg. 55 6 8 58 2 2 test light Max. 95 53 82 96 51 40 sources Min. 21 -38 -55 24 -40 -34 A previous study suggested that there are large mean hue angle (h) differences between CIELAB and CAM02 (especially for 190 < h < 290) and concluded that CIELAB has good lightness uniformity with poor hue uniformity, and CAM02 performs well in colour difference but has poor lightness and hue uniformity (Jin et al., 2009). Results from computations presented here supported this idea where variation in maximum and minimum lightness in CIELAB was very small (L*all/L*white = ~1) between all SPDs and “white” light sources, but variations in maximum and minimum a*-b* coordinates were greater (between 2 and 10 fold) than variations in maximum and minimum a'M-b'M coordinates in CAM02-UCS (between 1 and 3 fold). Maximum and minimum lightness variations in CAM02-UCS were moderate (0.4 < J'all/J'white < 1.87), but poorer compared to CIELAB.

Chromatic adaptation transform correction Hue angle anomalies at low tristimulus ratios have been previously reported for translucent objects (McLaren, 1980; Liu et al., 1995) and the use of chromatic adaptation transforms (CATs) are recommended for more accurate hue shift calculations (Li and Melgosa, 2012). A chromatic adaptation transform CMCCAT2000 (Li et al., 2002) was applied to CIELAB calculations to address this problem. CMCCAT2000 was found to outperform other CATs (Luo et al., 2003), and it has been previously used to minimise CIELAB non-uniformities (Davis and Ohno, 2010).

When test SPDs were limited to nominal “white,” hue angle (h) correlation between CIELAB and CAM02-UCS was improved. Figure 1 shows the hue angle and colourfulness differences between CIELAB and CAM02-UCS for a blue sample (sample 13) when the reference is CIE illuminant D50. Hue angles (h) were more varied in CIELAB compared to CAM02-UCS, especially when all SPDs were considered. Although hue angle in CAM02-UCS covered most of the hue circle (360 degrees) when all SPDs were considered, they were mostly concentrated on the dominant hue angle (e.g. h = 270 which approximates blue, as shown in Fig. 1a). Limiting

892 Proceedings of 29th CIE Session 2019 Durmus, D., Davis, W. EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02 the test light sources to close to the Planckian locus region decreased the calculated hue angle ranges both in CAM02-UCS and CIELAB.

Figure 1 – Hue angle ((a) and (b)) and colourfulness ((c) and (d)) values in CIELAB and CAM02- UCS calculated for all test SPDs ((a) and (c)) and nominally “white” light sources ((b) and (d)) respectively for sample 13

(a) (b) (c) (d) Similar to the hue angle, colourfulness in CIELAB showed larger variations compared to colourfulness in CAM02-UCS. Unlike the hue angle, limiting test SPDs to nominal “white” did not improve the correlation between colourfulness in CIELAB and CAM02-UCS.

In addition to the hue angle (h) and colourfulness differences, lightness, redness-greenness (a), yellowness-blueness (b) were compared to identify the underlying difference between hue shifts in CIELAB and CAM02-UCS based formulae. An example in Fig. 2 shows the correlation between redness-greenness (a), yellowness-blueness (b) in CIELAB and CAM02-UCS for a blue sample (sample 13) when the reference is CIE illuminant D50. Both redness-greenness (a) and yellowness-blueness (b) coordinates ranged more in CIELAB compared to CAM02-UCS when all test SPDs were considered. When test SPDs were limited to nominal “white,” a-b coordinate ranges were similar. When test SPDs were limited to nominal “white,” correlation between redness-greenness (a) improved (e.g. R2 = 0.662 for sample 13) more than yellowness-blueness (b) correlation (e.g. R2 = 0.002 for sample 13). The variation differences in coordinates (e.g. a*max/a'M,max ~= 140, a*min/a'M,min ~= 65, b*max/b'M,max ~= 12, b*min/b'M,min ~= 100 for sample 13) suggests that if there is a scale difference between two colour spaces, it is not linear.

Figure 2 – Redness-greenness coordinates ((a) and (b)) and blueness-yellowness coordinates ((c) and (d)) in CIELAB and CAM02-UCS calculated for all test SPDs ((a) and (c)) and nominally “white” light sources ((b) and (d)) respectively for sample 13

(a) (b) (c) (d) The correlation between CIELAB and CAM02-UCS lightness values were poor when all test SPDs were considered. Lightness in CIELAB (L*) were not limited between 0 and 100 due to the CMCCAT2000 correction. An example is given Fig 3. which shows the difference in lightness values between previous results and CAT corrected calculations across colour spaces for a blue sample (sample 13). In previous calculations, CIELAB and CAM02-UCS lightness correlation was low (e.g. R2 = 0.148 for sample 13) when all test SPDs were considered. Limiting test SPDs to nominally “white” increased the coefficient of determination (e.g. R2 = 0.695 for sample 13). When CAT correction was applied, the coefficient of determination increased even more (e.g. R2 = 0.881 for sample 13). The results suggest that CAT corrections increase the correlation in lightness between CIELAB and CAM02-UCS for only nominally “white” light sources.

Proceedings of 29th CIE Session 2019 893 Durmus, D., Davis, W. EVALUATION OF HUE SHIFT FORMULAE IN CIELAB AND CAM02

Figure 3 – Lightness in CIELAB (L*) and CAM02-UCS (J') calculated for all SPDs ((a) and (c)) and nominally “white” light sources ((b) and (d)) respectively, for sample 13, with ((c) and (d)) and without ((a) and (b)) chromatic adaptation transform correction

(a) (b) (c) (d)

4 Conclusion

Calculated hue shifts for chromatic samples may vary significantly under very similar test SPDs * (e.g. H CAM02,mod1 = 29 for two spectra that has a “good” spectral match according to goodness- of-fit coefficient GFC= 0.9994 (Hernandez-Andres et al., 2001)), which suggests a shortcoming of the hue shift formulae. To address this issue, hue shift calculations were performed in CIELAB and CAM02 with a large number of test SPDs and standard illuminant D50 and white pcLED references. Colorimetric calculations for all test SPDs and nominally “white” test light sources were compared to investigate the impact of colour space uniformity and scale on calculated hue shifts.

The results show that hue shift equations do not correlate well, even when light sources were limited to near-Planckian locus region (nominal “white”) and a chromatic adaptation transform was applied to CIELAB calculations. Results from the computations support the idea that colour space uniformity and scale might impact calculated hue shifts. The possible scale differences between redness-greenness (a) and yellowness-blueness (b) coordinates along the colour spaces were not linear. Lightness in CIELAB and CAM02 correlated well for nominally “white” light sources, especially when a CAT correction was applied to CIELAB. However, CAT correction caused irregularities (i.e. L* ranging beyond 0 and 100) when test SPDs were not close to the Planckian locus. Future work will investigate the visual assessment of hue shifts and test the performance of hue shift formulae.

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